1

Just Chat! / Re: The coronation of "eternal student", why was i not invited?

« on: Yesterday at 12:10:49 »

Hi.

   I'm not annoyed.    The last post was meant to be humorous it just evidently didn't work well, sorry.
I should probably be catching up on all the housework I haven't done while I was ill,  instead of posting too much for the next few days.   Meanwhile, I'm glad you're still OK but I should imagine you will need to keep taking it easy for a few more days.

Best Wishes.

2

Physics, Astronomy & Cosmology / Re: Why can't i understand the andromeda paradox?

« on: 05/07/2022 16:31:28 »

Hi.
    No worries @paul cotter ,  rest up and get well soon.
Best Wishes.

3

Physics, Astronomy & Cosmology / Re: Why can't i understand the andromeda paradox?

« on: 05/07/2022 15:00:42 »

Hi again.

    Well look, here's the thing from first principles...

    Start with a person called Paul on planet earth.   For ease of notation and calculation we will set up an inertial reference frame S  with co-ordinates (space, time) = (x,t) .  We'll only need one spatial dimension (just choose a Cartesian frame so that planet earth and the Andromeda galaxy lie along the x-axis).  We'll have Paul stationary in the frame S and, as usual, we'll put him at the origin.
    To keep it all simple, we'll have the Andromeda galaxy at a distance of  3 million light years from earth and we'll have it remain stationary in the frame S.     (In reality it's about 2.5 million light years away and you probably know it's on a collision course - none of that's necessary for the Andromeda Paradox, we just need it at a large distance).

    Let's draw a spacetime diagram now and put some important worldlines on it.


Andromeda1.png (12.8 kB . 1304x767 - viewed 397 times)

   Since Paul and the Andromeda Galaxy are stationary in this frame, their worldlines run parallel to the t axis.   Paul's is precisely along the t-axis.

    Now the general idea is that there are some Aliens living in the Andromeda galaxy and they will decide to invade earth.    Let's mark some important events on the spacetime diagram.     Event (x_A, t_m )   =   where and when the Andromedans have a meeting to consider invading Earth.       Event  (x_A , t_L ) =  where and when the Andromedans launch the invasion fleet.
   Paul considers events lying along the x-axis to be events occurring at time t = 0,  or  "right now".   So, for Paul,  the Andromedans are having a meeting to decide if they will invade.


Andromeda2.png (12.89 kB . 1304x767 - viewed 395 times)

   Now Paul has a friend,  let's call them Bicycle Brenda,  who is riding a bicycle past Paul at a low speed and just happens to be travelling toward the Andromeda Galaxy.   So Let's consider how Brenda sees the universe next...
   This is just standard stuff in Special Relativity,  Brenda sees Paul looking slightly thinner than if he was at rest,  this is length contraction  etc.   However, since the speed of Brenda relative to Paul is so small, it's not like this really matters or is significant.   Anyway, the easiest way to determine how Brenda sees the world is to construct another inertial frame around Brenda where she is the one at rest at the origin.   We'll set up a second frame S'  in which Brenda is at rest and at the origin.   We'll synchronise the times t and t' = 0 when Paul and Brenda are precisely at the same place (I'll say just passing each other but for the Mathematics it will fine if Brenda has ridden right through Paul at the event t=t'=0 and x=x'=0).   Anyway,  the frames   S with co-ordinates (x,t)   and    S'  with co-ordinates (x',t') are just Lorentz boosts of each other as usual,   with a tiny off-set velocity v = bicycle speed = 2 mph.

    We need the Lorentz transformations to see how the events in S are mapped to events in S',  we'll just focus on the time coordinate t'

t'  =   
   You can check this equation yourself, see https://en.wikipedia.org/wiki/Lorentz_transformation , for example.  Spend a moment and remind yourself how this equation can be used.    Given an event with values (x,t) specified in the frame S,   this equation determines the t' value that would be assigned to the corresponding event in frame S'.    We could determine the corresponding x' value with another equation - but we won't need that for this example. 

    Brenda considers all events in the universe to be happening "right now"       if and only     they have t' coordinate = 0 in the frame S'.    They can have any  x' co-ordinate (that just tells her how far away the events are in space),  just so long as  t' =0  (that means they are happening at t'=0 or right now, where "now" means when Brenda passed Paul and said "Hi!"  or  "Sorry I just ran you over" etc).
    We want to mark all the events on our spacetime diagram that are happening right now for Brenda.  However, our spacetime diagram only has an axis marked up for the frame S.
    Set t'=0  in the above Lorentz transformation equation and determine the set of all events (described with co-ordinates  x,t in S) that are happening "right now" for Brenda,  that's what we will mark on our diagram.

   From the Lorentz transformation equation we obtain:
0 =  t'   =      
   ≠ 0    ,  so divide ,   re-arrange and obtain 

  t' = 0        <=>        t = 

On the R.H.S.   we have the relationship  between  t and x  (the co-ordinates in S  that describe events happening now throughout the universe for Brenda.
    v =  small positive value =  bicycle speed in S and it's in the +ve x direction.
    c²  =  a massive number.

v/c²   is therefore a tiny positive number.      t =    (v/c²) . x   describes a straight line on the diagram that is almost parallel to the x-axis.   However the key is that it is NOT quite parallel to the x-axis, it is angled upward a tiny bit.   Moreover the Andromeda galaxy is a long way along the x-axis, so let's  put this line of constant  t'  on our spacetime diagram and see what happens.....


Andromeda3.png (16.34 kB . 1304x767 - viewed 399 times)

   The Green line shows all the events throughout the universe that are happening now (t'=0) for Brenda.
Hopefully you can see that, as far as Brenda is concerned, when she passed Paul and said "Hi!"  the invasion from Andromeda has been launched.   Meanwhile, for Paul the meeting to decide whether to invade Earth or not hasn't finished yet.

Anyway, I hope that will help to see the gist of the argument for the Andromeda paradox.
As @Halc mentioned earlier,   you need to be carefull not to say,  Brenda "sees" the invasion has been launched.    There's no way light has reached Brenda's eyes yet, she isn't going to "see" the ships coming.   It's only that the launch is actually happening now for Brenda even though there is no practical way she could know.  So, for example, she couldn't tell Paul that it was coming.... unless she has some  extra-sensory perception and says "you know, it's funny but every time I ride my bike in that direction I just feel like some invasion has been launched".  In which case Paul would reply, "have you tried changing to a lower gear?  You might be getting yourself a little out of breath and dizzy".

Best Wishes.

4

Physics, Astronomy & Cosmology / Re: Why can't i understand the andromeda paradox?

« on: 05/07/2022 12:52:43 »

Hi.

    Hope you are well.   This is is obviously one of the most interesting posts available today.  I have a strong suspicion that @Halc is about to write a post since the forum is reporting him as viewing this post at the moment.    He obviously has a head start over me, so I'm just going to wait and see what gets done.
      For the short term, I'm just going to glance through some YT videos that might exist and see if I can recommend one.

Best Wishes.

5

New Theories / Re: How Many Numbers Exist?

« on: 03/07/2022 03:26:19 »

Hi.

Is there a set of numbers which contains more than algebraic numbers but less than real numbers?

   If you just want a SET of numbers,  yes,  many of them.
There's an infinite set of distinct transcendental numbers,   T.   These are real numbers that are not algebraic.   Actually MOST of the real numbers are these,   the algebraic numbers are countable so they are a tiny drop in the ocean compared to the transcendental numbers.
   Anyway, you could just keep adding the transcendental numbers one at a time until you got bored.

   You can cut down some of those intermediate sets of numbers if you put more of a restriction on your set of numbers.   For example, instead of just asking for a set of numbers, insist that the new set of numbers is always a proper Field in its own right.   These would be called Field Extensions.   (Example:   If you try to add π,  then the field operations automatically generate  π², π³, ....,  1/π, ...., -π, .... (705 + 3/π), ....   so  to ensure the set really is closed under field operations you'd need all of these numbers added in one go).
  None the less, I still think there's an infinite set of simple field extensions you could find.  (I haven't spent too long thinking about it but I reckon you could try a simple field extension by adding π and show that √π is still missing,  so extend again with √π and show  the √(√π) is still missing..... etc.....    the root of what you've just extended with should always be missing).

Best Wishes.

6

Physics, Astronomy & Cosmology / Re: What is a black hole made of?

« on: 27/06/2022 19:01:32 »

Hi.

   Is David joining us as a member on the forum?   You could use a false name etc.   Anyway if you aren't, then your answer will be be available in a podcast shortly.   If you are joining us then please say something here and we'll have a discussion.

Best Wishes.

7

Physics, Astronomy & Cosmology / Re: Why is inflation needed in the bbt?

« on: 25/06/2022 15:32:44 »

Hi.

from an engineering perspective(which is what I am limited to) ∇.b=0 precludes the possibility of magnetic monopoles.

   Yes, more or less.

   We haven't observed any magnetic poles,  that is written in mathematical notation as  ∇.B  = 0.
That's all that is,  just a way of writing that phrase in mathematical notation.   It's not a proof that magnetic monopoles don't exist.    If they were found, then that equation in the set of Maxwell's equations would need to be changed. However, it would only need changing for those situations where there is a magnetic monopole in the experiment or situation being modelled.    Where there isn't any magnetic monopole then the equation obviously still holds.
   The existing theory of classical electromagnetism can be considered as some "proof" or evidence that magnetic monopoles are very rare and certainly don't contribute to many situations.   Maxwell's equations including  ∇.B  = 0   have proved very accurate and reliable in predicting and modeling electromagnetic phenomena.   If  ∇.B  is significantly not 0 in some situations we should have noticed it by now because Maxwell's equations would have given us predictions that didn't match the observations.
     However, that's as much as we can say - if they exist, then they will be rare and not important for the situations we have studied or modelled so far.   ∇.B(x, t)  ≈ 0   at all positions x in space and times t   should remain a very useful approximation.

I would love to hear some elaboration on this, in particular why the bbt requires these monopoles.

    It's not exactly the Big Bang Theory that demands monopoles.   The existence of magnetic monopoles is suggested by several more specific theories in physics.  For example, standard particle theories and superstring theory.   Of which the standard model of particle physics is probably the most important and most widely accepted, superstring theory is an optional addition. 
    So it's possible to imagine that the bare-bones of the ideas for the BBT could persist while some of the fine details for things like particle synthesis just after the Big bang are adapted.   Physicist's would like to find monopoles because that would support the overall conglomeration of ideas that make up our best theories of cosmology including things like particle synthesis.   These early moments of the Universe including processes like nucleosynthesis are all included under the umbrella term "the Big Bang Theory".

Best Wishes.

8

Physics, Astronomy & Cosmology / Re: Is the inverse square law only approximately correct in general relativity?

« on: 25/06/2022 14:33:45 »

Hi.

     I'm always very grateful for anyones time spent in conversation.  So thank you very much @evan_au.
However, I can't always agree with everything and that is the nature of discussion after all.   What you've said isn't wrong, it's just misleading.   Although, equally, what I've said before could be considered misleading.
    We need to establish a few things and then hopefully we will be seeing and understanding the same things.

I was not thinking about a horizon at a fixed distance.

   OK  -  BUT you should be.    The inverse square law is about the intensity received at a distance, r, from the source.   That is a physical distance, so it is determined by the metric.   It is not determined by reference to a difference in the values assigned to locations in the co-ordinate system we commonly use to describe an expanding universe.
   The usual co-ordinates used in an expanding universe are the called the co-moving co-ordinates.  Galaxy 1 can have fixed co-moving co-ordinates and it's tempting to say it has a fixed position.   Galaxy 2 can also have fixed co-ordinates and we can be tempted to say it has a fixed position.    The co-ordinate differences between the galaxies never changes, so that seems fine.   However, the physical distance between the galaxies is increasing with time,  in that respect it doesn't look like the galaxies are fixed in position in any ordinary sense of the word.   To avoid the confusion, it's best if you just don't say or imagine that either of the galaxies have a fixed position.   Instead, just say that the galaxies are "co-moving with the universe",  or  that they are "co-moving" for short.

But space can expand faster than c, so (in principle) there are distant galaxies that people on Earth could see today, but
 which will not be visible in 10 billion years, because the expansion of space has carried them outside our visible universe.

      This is correct.   However, the light emitted by the distant galaxy will travel an infinite physical distance.   It's just that how far it can go in 1 unit of time will not be sufficient to match the expansion of space that is occurring between the distant galaxy and earth.
      We would place our sphere, where the intensity is being determined, at a fixed physical distance from the distant galaxy and not at a fixed co-moving co-ordinate separation from the distant galaxy.   The light from that distant galaxy will reach the surface of that sphere.    Just to get the image and understanding right,  the surface of that sphere might have started at time t=0 precisely where planet earth was.   However, the surface of that sphere will be a long way from earth at a later time t=1 unit,  when the photons from the distant galaxy finally cross over that sphere.
     We can place a sphere with a fixed physical radius, r, around the distant galaxy (it doesn't matter how large r is)  the photons from that galaxy will (eventually) reach the surface of that sphere.   In no way does this contradict the idea that the photon won't reach earth - the surface of the sphere is nowhere near planet earth when the photons cross over the sphere.

If you posit some particle that travelled at c/10 (and didn't slow down), there would be regions of our visible universe that could never detect these particles, because the space in between is/will be expanding faster than c/10.

   Yes, total agreement.   However, that has nothing to do with the particles crossing over a sphere at some fixed and pre-determined physical distance from the source.

Best Wishes.

9

Physics, Astronomy & Cosmology / Re: How does special relativity explain dimensional components ...

« on: 25/06/2022 13:02:01 »

Hi.

Does time and space have separate components like that?

   Yes and No.

The yes bit:
    4-vectors are what are important in spacetime.    These have 4 components,   3 of them are called spatial components and the other component is called the time component.  You can write the spatial components first and the time component last but it's more common to write the time component first.   It's also fairly common to start numbering the components from 0 and not from 1.   The final slightly confusing thing you might see is that if you had a 4-vector  X   then you may see the components written as  X⁰,  X¹,  X²  and  X³.    Superscripts instead of subscripts like  X₀,  X₁  can be used.
    For example    r =    ( ct,  x,  y,  z)  is the usual way of writing  the position 4-vector of an object.    It has a time component  ct  =    c (the speed of light)  multiplied by the position of the object on the time axis, t.    It has spatial components   x, y, z   which are the position of the object along the x, y and z axis respectively.    Now you could use t as the time component instead of ct but the algebra turns out to be much easier if you use  c (the speed of light) multiplied by t   as the time component.

The "no" bit
1.   There's an unusual way of determining the magnitude of a 4-vector.  You might see it called the "norm" or "Minkowski norm" of a 4-vector.    For simple vectors used in Euclidean space or Newtonian mechanics,  whenever you increase the size of one component the overall magnitude of the vector would increase.   For 4-vectors that's not always the situation,  you can increase the size of one component and end up reducing the overall magnitude of the 4-vector.    The Minkowski metric is described in various places  [For example,   https://phys.libretexts.org/Bookshelves/Modern_Physics/Book%3A_Spiral_Modern_Physics_(D%27Alessandris)/3%3A_Spacetime_and_General_Relativity/3.1%3A_Minkowski_Metric  ].

2.   You are mainly discussing velocities and motion in your posts, rather than just positions.   In ordinary Newtonian mechanics, velocities are just a rate of change of position with respect to the time co-ordinate.   For 4-velocities we can't determine rates of change with respect to a fixed time co-ordinate,  instead we must determine rates of change with respect to what is called the proper time for that object undergoing the motion.
   What this boils down to is that spatial components of the 4-velocity are NOT exactly the spatial components of the ordinary Newtonian or 3-velocity that the object might have.   Instead the spatial components are a multiple of the spatial velocity you would have assigned the object in Newtonian mechanics.  Also it's not a fixed multiple,  the multiple changes according to the Newtonian 3-velocity of the object.    Specifically, the  spatial components of the 4-velocity are given by   γ  (the gamma factor) multiplied by the spatial components of the 3-velocity.

- - - - - - - -
     That might be more detail than you were after.   Overall there is a lot of similarity between  4-velocities used in Special relativity and more conventional velocity vectors you might have seen in Newtonian mechanics.    I've mentioned the differences because, in my limited experience, if we don't then it's human nature to run away with the idea that it's all exactly like Newtonian mechanics and ordinary 3-velocity vectors.   You'll soon hit problems if you do that.
     For example,  it can be useful to consider the magnitude of a 4-velocity vector.  An ordinary object with some positive rest mass always has a 4-velocity vector of magnitude c (the speed of light).   That magnitude can be shared out between the time component and the spatial component of the objects 4-velocity.   An object at rest (in a given frame which we will use to assign the velocity vector) has all of its velocity in the time component while the spatial components would have the value 0.     Meanwhile, an object in motion (in the given frame) has a non-zero value in the spatial components of the 4-velocity and a correspondingly lower value* in the time component.

Best Wishes.

* LATE EDITING:  I don't like this on a second reading.   It's precisely one of those examples where you could have a larger numerical value for the time component but that is actually reducing the overall magnitude of the 4-velocity and not increasing it (because the Minkowski metric subtracts the time component instead of adding it).  It's fair to say the object has less velocity through time and many Pop Sci articles will do this - but it's not correct to imply that the numerical value you find written in the time component of the 4-velocity has to be smaller.

10

Physics, Astronomy & Cosmology / Re: Why is inflation needed in the bbt?

« on: 24/06/2022 15:19:48 »

Hi.

The short article provided by @Origin  is extremely good.   It sets out the three main problems and explains how inflation solves these:

1.  That space does seem to be almost flat.

2.  That distant parts of space seem to be at similar temperatures, suggesting they were in thermal contact at some time.  Ordinary big bang expansion would have kept them apart and kept driving them apart faster than light could have travelled from one region to the other.   No exchange of heat between them should have occurred.  Without inflation, the only possibility is to assume that it was coincidence that all these regions had the same temperature after the big bang.  (That isn't an impossible coincidence, if the Big bang was very symmetric you might get something like that - but it's an assumption that you just don't need to make if the regions were in thermal contact with each other).

3.    Lack of our ability to find magnetic monopoles.

We can probably add two extra problems / observations:
4.    That space is surprisingly homogeneous and isotropic -  it's much the same density everywhere and in every direction.   With inflation you don't need to assume it was always this way just after the big bang.   A massive expansion of a less homogeneous space produces a large region where everything is much more homogeneous.
5.    Conversely, it isn't completely smooth.   There are small irregularities in density and this is what ultimately gives rise to the clumping of matter  -  the formation of galaxies in some places and voids in other places.   

   How 4. and 5.   work together is quite interesting.   They aren't really opposites of each other.    Assume the situation described by 4. happens: 
(i) The lengths over which differences are observed increases - differences in densities observed over a length of say 1 light-second are now only noticeable over a distance of 100 light seconds.
(ii)  The actual size of the density differences is also reduced:  Since the volumes of space were stretched the actual densities are brought closer to 0, so the difference in densities is reduced.
    This sort of change keeps happening.  Meanwhile there will always be small quantum fluctuations happening - things that might produce a difference in density that are observable at lengths of a (tiny) fraction of a light-second.   However, these small changes that were due to quantum fluctuations get stretched and eventually become density differences that are noticeable over lengths of about 1 light-second.  This whole thing keeps going and repeating (it's not a discrete, first this, then that,  it's a much more continuous thing but seeing it as series of small discrete steps is just easier to visualize).    Overall,  the coarse and large scale differences in density keep getting stretched and smoothed away, while the quantum fluctuations keep getting magnified to produce small differences in density that are noticeable over lengths of about 1 light-second.    We end up with a situation where the small differences in density that we want are assured while larger or more coarse differences are equally assured to have been removed.  "We want" these small differences in the sense that these do work well in the models and simulations for galaxy evolution.

    That's about it.   That's the limit of my understanding about inflation.   Sources of information were:
a)  "The History of the Universe", especially Chapter 13,  David H Lyth,  Publisher: Springer,  2016.
b)   NASA website provided by Origin earlier.
b)   Wikipedia:  https://en.wikipedia.org/wiki/Inflation_(cosmology)

A final note worth mentioning is that Inflation remains an optional addition to the Big Bang Theory:
The basic inflationary paradigm is accepted by most physicists, ..... however, a substantial minority of scientists dissent from this position       [Quote from Wikipedia]

Best Wishes.

11

New Theories / Re: Did we really never observed white holes ?

« on: 23/06/2022 23:36:28 »

Hi.

   I'm sorry but I am struggling to understand what has just been said.   Some bits of it do look like existing ideas for white holes.

Best Wishes.

12

New Theories / Re: Can conscious thought act on matter?

« on: 23/06/2022 23:26:31 »

Hi.

I read most of what was written just above.   It says quite a lot of stuff   BUT  none of it seems to be useful.  It doesn't make any predictions or suggest something that can or should be tested.   Science is less concerned about why or what some ultimate truth might be and more concerned with having an explanation and a model that is useful for making predictions.   

Best Wishes.

13

Physics, Astronomy & Cosmology / Re: Is the inverse square law only approximately correct in general relativity?

« on: 21/06/2022 18:46:50 »

Hi.

I see a dimensional conflict...

   Yes.   I almost mentioned this in the post but it was already too long - because all good scientists are trained to check the units and dimensions.

The metric has a form where φ actually has dimesnions of length:

ds²  =     (stuff with an overal dimension of length²)  +  Sin²(θ) dφ². 
We'll leave the θ as a dimensionless angle,   then the  dφ² must have dimensions of length².
 
   Anyway,   In the final expression for the surface area  4πr,     that is   really   2 . (2π) . r    where the  (2π) has dimensions of length.

Best Wishes.

LATE EDITING:  Having a dimension assigned to what looks like an angle can seem very hard to swallow.   If it helps, the space can be considered and conceptualised as something with flat (2-D)  polar co-ordinates  (r, θ)  and a third dimension φ which is the depth into the page.   The depth into the page just happens to permit a range between 0 and 2π.   That helps to see φ as something that can have dimensions of length.   As I mentioned, there's no good way to visualise this very non-Euclidean space and re-drawing everything with that sort of representation just strains understanding elsewhere.

14

Physics, Astronomy & Cosmology / Re: Does The Gravity Of A Black Hole Travel Faster Than The Speed Of Light ?

« on: 15/06/2022 02:02:07 »

Hi.
   Thanks for the extra information, @evan_au .  There's stuff I didn't know there and I may look into Supernova again to see what the latest is.   
   The rest of this post may look like a criticism, sorry.  It isn't meant to be.

Time dilation is so extreme within millimeters of the event horizon that the image of an infalling rock would be very quickly red-shifted into oblivion.

    I think we need to establish where the observer is and assume they are using a frame of reference where they are at rest.   The distant observer = An observer at a fixed radial co-ordinate, r >> Schwarzschild radius.      The rock = the rock or anyone close to the rock and falling in with it.

      We all agree that the rock doesn't spend long outside the event horizon, it just falls in within a finite amount of time as far as its concerned.   However, for the distant observer the rock takes an infinite amount of time to reach the event horizon   (well, certainly if the rock is treated as such a small mass that it doesn't affect the spacetime geometry - a previous post discussed that and mentioned my uncertainty about it).
     As far as the distant observer is concerned, light from the rock is progressively red-shifted and total luminosity from it reduces.   This isn't a quick process.

So: Very few photons, severely red-shifted: The rock would not "float" near the event horizon, it would just disappear.

   Bits of this are OK.   However, it doesn't "just disappear", it fades away.  It's like having a studio engineer with the slowest hands in the world, turning the fader knob so slowly that the universe will end before the stage actually goes dark. 

...forming a black hole, with almost the same mass as the star before it imploded...

    Is that right?  I know stellar collapse varies quite a lot and I'm not aware of the latest ideas for the typical behaviour.   Old texts used to suggest that typically there is a supernova explosion where the outer layers of the star making up about 20% of the original mass of the star is blown away.    Some sources put the amount of matter ejected far higher than that...
About 75% of the mass of the star is ejected into space in the supernova.   

https://imagine.gsfc.nasa.gov/science/objects/stars1.html

Best Wishes.

15

Physics, Astronomy & Cosmology / Re: Does The Gravity Of A Black Hole Travel Faster Than The Speed Of Light ?

« on: 14/06/2022 18:26:02 »

Hi.

Something must be holding light back faster than light itself travels.

    Not really.    The easier way to imagine what is happening is to assume space itself is being pulled in toward the black hole singularity.   So light is travelling as fast as it can through space but it's not good enough, space itself is being pulled into the singularity faster than that.
    This is only an image or conceptual representation but some people have presented the idea as water flowing and people trying to travel through the water.   There's a reasonable animation on YouTube that I'll try and find and add to the post later.

LATE EDITING:   I can't find it in isolation.   You can see it in this video by Brian Greene,   "your daily equation #31", available on YouTube.      Aim for the time   between   4:20   and  6:00.

so it's the propagation of internal gravity waves that stops light ?

   No.

does light even exist inside a black hole ?

   According to theory,  yes it can   (for a while before it hits the singularity).   No one has actually been in there to see it.

Best Wishes.

16

Physics, Astronomy & Cosmology / Re: What are the properties of space?

« on: 13/06/2022 16:28:52 »

Hi.

    I fully understand your comments, @paul cotter  .    Replies are always optional.   The forum is meant to be for interest and when it starts to feel like an obligation or burden then it's time to re-examine what you're doing and why you think you should.
      The comment you made about the metre is a perfectly good one.   However the idea of defining a metre by as how far light travels in 1 / 300 000 000   th  of a second* isn't completely silly or arbitrary and it does open the door to looking at things in different ways.   That means a few more minutes of hopefully interesting discussion, if nothing else.
*LATE EDITING:  Yes, it's actually 1/ 299 792 458  - it's just that the exact numbers aren't important and get in the way of the general idea.

      For example, how would you realistically measure big distances?    Presumably with a radar or laser measuring device,  you'd just time how long it takes to get a signal back.    How would you know if the distance between two objects has increased after 100 years, or if the speed of light has actually decreased as time evolved?    More significantly, would there be any difference to how physics behaves?  These ideas are always worth a moments thought and well worth revisiting every now and again.   Usually you can discern a difference between distance increasing and light slowing down but it get's murky again if you consider that maybe your measurement of  time is also changing.  Maybe there are some important dynamic fields in the universe and the frequency of radiation emitted by Caesium-133 atoms is changing as a result of that, so that the atomic clocks used to define the second are not actually keeping the correct time.
     For simplicity, we can consider trying to view the universe from some other place or point of view.   One easy option is to adopt the language used by those who suggest our Universe might be a giant simulation (much as if it's running on someone's laptop).   If their laptop starts to run more slowly (perhaps because the processor is overheating and it gets throttled-back) then they notice that our ideas of time have changed, it takes longer to get their action hero across a room.   However, the simulations don't notice any difference, everything in the simulation moves slower in the correct proportion.    Similar things happen if distances suddenly doubled (in all directions) but everything can move twice as fast as before.   The computer simulation action hero can still fire an arrow across the room in the same time.   
    Overall then, you have to decide that something(s) is (are) "locked down" or held constant.   Typically you'd start with time and assume the simulations have some awareness of a flow of time and it doesn't matter if it changes relative to the gamer's time outside the laptop, it's constant and fixed for the simulations.  Then build up from there systematically, considering if it's possible for something else (like the speed of light inside the simulation) to change or if it would be indistinguishable from some other combinations of things changing.

Best Wishes.

17

Physics, Astronomy & Cosmology / Re: What are the properties of space?

« on: 10/06/2022 20:58:39 »

Hi again.

What are the properties of space?

    I don't know.   You ( @paul cotter ) probably need to start by examining what you consider to be space.   Some of the previous posts have done a bit of that - but what do you think or want to consider as space?
    One thing that hasn't been discussed is whether space is continuous or discrete.   Is there a smallest unit of length?   (or a smallest unit of time?)    If there is then a lot of our ideas about the geometry or inherent properties space aren't quite right.  For example, Special relativity and its predictions of length contraction are in trouble.

I can only think of two, c (itself a composite of permeability and permittivity) and G

   You seem more interested in the fundamental physical constants rather than anything else about space.    There's a bit of discussion about what the fundamental constants are or should be in Wikipedia:   https://en.wikipedia.org/wiki/Physical_constant#Number_of_fundamental_constants .        G  and c  which you suggested do get into that list.   There are some complications, for example the way the speed of light, c, and "the metre" has been defined in the SI units has been modified a few times and now it's not possible to adjust c,  instead you would be adjusting the metre or challenging the time interval of an Atomic clock based on Caesium.  So some would say that to adjust c, you need to go at it indirectly by doing something like adjusting the fine structure constant.   
   Basically, identifying the fundamental physical constants is a contentious issue and if we discover more physics, there's likely to be more fundamental physical constants required.

Best Wishes.

18

Physics, Astronomy & Cosmology / Re: What are the properties of space?

« on: 10/06/2022 01:43:42 »

Hi.

Space is what separates bodies of stuff.

   Yes.... and also time does that.   Two bodies can be in the same space but at different times.    As I'm sure you know, there's sometimes no difference between space and time separation except which frame of reference you use.

we can certainly describe the static (fields) and dynamic (particles and waves) contents of regions of space. So if you want to be philosophical you could describe the ability to contain such phenomena  as a property of space, but I suspect this is a sterile  intellectual cul-de-sac.

    Well, I was tempted to go down those lines.   There are various fields defined on space and assumed to exist throughout all of space.  That does seem important and essential that space can support this.
     Another important thing about space is that it has some inherent structure.   I would be tempted to say mathematical structure but let's get things in the right order:  Our concepts and development of mathematical structures were obviously influenced by the way space seems to be.   If space had been different, you can be pretty sure we would have developed different ideas of geometry and such like.   So the only important thing is that space does seem to have some inherent structure and properties - something that we will ultimately call geometry, the properties of a vector space, topology  etc.
     I'm biased toward favouring General relativity, so you can tell where I'm going with this....  the metric seems to be an inherent property of space.

@geordief ,  sorry your post appeared after I had started writing and it's too late to reply to all of that today.

Do we just start with what we observe and not try to second guess  what is out there and in here?

    That isn't the human way.  We are very inquisitive.   You've just asked plenty of questions for example.

Best Wishes.

19

General Science / Re: What is the actual Brayton Cycle efficiency?

« on: 09/06/2022 23:01:43 »

Hi.

Nobody seems to be rushing to help.

   I don't know enough about turbines.   This website looks authoritative  (It's got an mit.edu domain name) and supports the formula  you ( @futur123 ) and also you ( @paul cotter  ) have suggested,   given some re-shuffle or proper presentation so that you can see what divides what.



with the points  a,b,c,d  as identified on this   P-V  diagram:


Best Wishes.


    Reference:  equation  (3.8 )   on  this  website:    https://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node27.html

20

Physics, Astronomy & Cosmology / Re: What are the properties of space?

« on: 09/06/2022 16:57:14 »

Hi.

...but even space itself is undefined in the absence of something to occupy it...

    Space is just a set of points in a co-ordinate system.   

The Schwarzschild solution of the EFE is a vaccum solution.   It has infinite space and nothing material in it.
The Milne Model, which you (@ Halc ) are fond of pulling out as an example to generally foul things up when required,  that's another vaccum solution with infinite space.
Minkowski Space is another example (which isn't different from Milne, it just has a different co-ordinate system).

A property of our space is that it is 3 dimensional...

   Yes, there aren't any string theorists on this forum.

I'd say both are a set of constants (tunings) to our physics, along with a fairly short list of other constants, but these define how our physics works as compared to the behavior of the same physics with different constants.

   Yes.... and exactly this sort of thing is done.   Physicists do consider how the universe might be different if we adjust the value of certain key constants of the universe.
   Our universe seems to be finely tuned for the development of life, for example.    Before getting too complicated and trying different values for some constants,  we can even consider what happens if there are less than 3 dimensions,  say only 2 spatial dimensions.   Then  organisms can't evolve which have a digestive system with an entrance (a mouth) and a separate exit (let's call it an exit),  since that will inevitably cut the organisms into two separate bits - two organisms.   This alone is thought to seriously limit the complexity of life that can evolve.
      It's also possible to adjust the constants in such a way that some physics effectively disappears.   For example, if we put the constant c → ∞  then we can still have special relativity but it's just that it doesn't matter anymore.   Length contractions and time dilations become 0   etc.   It is as if the effects of special relativity have gone and we have Gallilean relativity.    We do also get some unusual and possibly undesirable consequences,  for example every point in spacetime is causally connected to every other point in spacetime - but there's no reason to assume that just because some thing can move at an arbitrary speed it will,  there may still be a practical limit for the speed of anything and hence a practical limit on causality.
     Anyway, just as we can make some physics become less important  (e.g. SR disappears as c→∞),  we can imagine that there are already some laws and some constants that are so small (or so large) that some physics has effectively been hidden from us.  Change those constants and we experience some new physics that we were unaware of.

What are the properties of space? I can only think of two, C(itself a composite of permeability and permittivity) and G. In thermodynamics two independent properties can define a system(in equilibrium), is there any correlations here.

    Well, on a vaguely similar line of reasoning....   Energy is or was thought to be one of the most important things in Physics.   There are several ideas about the universe being in an equilibrium of different sorts of energy.   You ( @paul cotter ) started a recent thread about this and had replies like this one from me:
https://www.thenakedscientists.com/forum/index.php?topic=84890.msg679741#msg679741
     Where Stephen Hawkings put up some ideas and discussion.

...this is wooly thinking, no doubt about it.  However I have often been asked an utterly stupid question and in the process of untangling what the other person actually wanted to know I have learned a new perspective on the matter in question. 

    Sounds fine to me and there's every reason why something like this should be discussed.
If it gets too woolly or speculative,  then it might be better off in the "Just Chat" secton or the "New Theories" section, or somewhere like that.    I'm not a moderator and I don't mind, it's just that it's difficult to apply one rule for person X and another for person Y.   So don't be too surprised or disappointed in some way if this thread does get re-located eventually.   Personally, I like an open-ended "what-if" and  "what may come of this"  discussion about science and I think it's exactly what a forum can and should offer - but this isn't my forum and there are some rules and policies.   Otherwise the main sections are filled with junk etc.

Best Wishes.